Learn Hardcore Icelandic: Mengunin er verri í dag en í gær. - The pollution is worse today than yesterday.

So Mengunin er verri… literally: “The pollution is worse…”.
Using the definite form suggests you are talking about a specific, known pollution situation (for example, the pollution in your city).

Why is the article attached to the noun (mengunin) instead of a separate word like “the”?

Icelandic normally does not use a separate word like English the.
Instead, it adds a definite ending:

masculine: bíll → bíllinn (car → the car)
feminine: bók → bókin (book → the book)
neuter: barn → barnið (child → the child)

Here mengun is feminine, so the nominative singular definite ending is -in:

mengun → mengun
- in → mengunin (the pollution)

What word is verri derived from, and why doesn’t it look like it?

Verri is the comparative form of the adjective vondur (also closely related to illur), both meaning bad.

It’s an irregular comparison:

vondur – bad
verri – worse
verstur – worst

This is very similar to English bad – worse – worst, where worse does not look like bad either. So verri works just like English worse here.

Why is it verri and not some other form like verra or verr?

Adjectives in Icelandic agree with the noun in gender, number, and case.

mengunin is:
- gender: feminine
- number: singular
- case: nominative (it’s the subject)

So we need the feminine nominative singular form of the comparative verri, which is:

masculine nom. sg.: verri
feminine nom. sg.: verri
neuter nom. sg.: verra

Since mengunin is feminine, we choose verri, not verra.

If the subject were neuter, e.g. loftið (the air), we’d say:

Loftið er verra í dag en í gær. – The air is worse today than yesterday.

Could I say Mengunin er slæmari í dag en í gær instead of verri?

You can, and it is grammatically correct:

slæmur – slæmari – slæmstur (bad – worse – worst)

But in this kind of sentence, verri is usually more natural and idiomatic.
Rough guideline:

verri (from vondur/illur) is very common and neutral for worse, especially in comparisons like this.
slæmari can work, but some speakers might feel a tiny nuance of “of poor quality” / “not good” rather than the very broad “worse” that verri has.

So: Mengunin er verri í dag en í gær is the most typical phrasing.

What exactly does en mean here, and how is it used?

In this sentence, en means than and is used after a comparative:

verri en – worse than

Structure:

[comparative adjective] + en + [thing you compare with]

Some examples:

Hún er eldri en bróðir hennar. – She is older than her brother.
Bíllinn minn er dýrari en þinn. – My car is more expensive than yours.

En is a conjunction here, not a preposition, and it does not assign a case. The phrase that follows simply has whatever form it normally has (here: í gær as a fixed time expression).

Why do we say í dag and í gær, with í (“in”), when English just says “today, yesterday”?

Icelandic usually uses prepositional phrases for days like “today / tomorrow / yesterday”:

í dag – today (literally: in day)
í gær – yesterday
í fyrradag – the day before yesterday
í daginn – earlier today (more specific, “in the course of today”)

These are set expressions. You almost always need the í in normal sentences:

Ég kem í dag. – I’m coming today.
Það var kalt í gær. – It was cold yesterday.

Native speakers experience í dag and í gær almost like single adverbial units (time adverbs), even though they’re formally preposition + noun (/historical noun).

What case is dag in í dag, and what about gær in í gær?

The noun dagur (day) declines like this in the singular:

nominative: dagur
accusative: dag
dative: degi
genitive: dags

In í dag, the preposition í takes the accusative when talking about a time span / point in time, so dag is accusative singular.

For í gær:

Historically, gær comes from a word meaning “yesterday.”
In modern Icelandic, gær is felt as a fixed time word (an adverb), especially in í gær.
You don’t generally treat it as a freely declining noun in everyday grammar.

So:

í dag – í
- accusative noun dag
í gær – fixed expression with gær functioning like a time adverb.

Can I drop the í and just say Mengunin er verri dag en gær?

No, that would be wrong in normal Icelandic. You need í in both phrases:

Mengunin er verri í dag en í gær.

You can sometimes omit the second í in very informal or fast speech:

… verri í dag en í gær. (full, careful form)
… verri í dag en í gær. (same in writing; in speech some people “swallow” the second í, but it’s still understood)

You cannot omit í entirely the way English omits a preposition with today and yesterday.

Could I move í dag to the front and say Í dag er mengunin verri en í gær?

Yes, that’s perfectly correct and very natural:

Í dag er mengunin verri en í gær.

Word order in Icelandic is relatively flexible for adverbs like time expressions. Both are fine:

Mengunin er verri í dag en í gær.
Í dag er mengunin verri en í gær.

The second version puts extra emphasis on today (“As for today, the pollution is worse than yesterday”).

How do you pronounce Mengunin er verri í dag en í gær?

Approximate pronunciation (IPA, using a common Reykjavík accent):

Mengunin – [ˈmeŋ.kʏ.nɪn]
er – [ɛr]
verri – [ˈvɛrɪ]
í – [iː]
dag – [taːɣ] (initial d often pronounced like t, final g as a voiced velar fricative)
en – [ɛn]
í – [iː]
gær – [caiːr̥] or [jaiːr̥] (palatal or y‑like onset, ær roughly like “ire” in tire, but shorter and tenser)

Main stress is on the first syllable of Mengunin and verri, and each content word has its own stress.